Yellow sticky note in the wind
Final:



Scene setup:



Plane (table).

This is just simple Plane with added Collision (default setup). It should be a little bit below sticky note.

Sticky note.

Another Plane, Subdivided with Weight Paint and Cloth physics.


Weight Paint - Red color is 'sticky' part, green is still little stiff and blue for full influence. You can paint it differently if you want.
Cloth physics - main goal here was to make it light and stiff.




Quality - 20, for better overall animation and smoothness,
Mass - 0.1, Wind and Gravity influence,
Structural, Bending, Spring - 400, 500, 50, all for getting rid of small wrinkles,
Air - 4, it will slightly increase air resistance and smooth wind influence,
Pinning - Group, most important thing here, this one will take Weight Paint as stiffness map,
Cloth Collision > Quality - 4, for better collision with table.

Force Field > Turbulence - this one could be Wind or probably something else. Adjust Strength, Noise as you like, but keep Size at 10. You can animate position of it and also Strength and Noise. Additionally you can add more of them with different settings.